A $7.000principal is invested in two accounts, one earning 3% interest and another earning 7% interst. If the total interest for the year is $262 then how much is invested in each account?

Let the investment in first account be x and this account is earning 3% interest

So Interest on this account is 3% of x = 0.03x

So the investment in second account would be (7000-x) and this account is earning 7% interest

So the interest on this account is 7% of (7000-x) = 0.07 * (7000-x)

Given that total interest for the year is $262

So we have

0.03x + 0.07 (7000-x) = 262

0.03x - 0.07x + 0.07*7000 = 262

-0,04x + 490 = 262

-0.04x = 262-490

-0.04x = - 228

0.04x = 228x

x = 228/0.04

x = 5700

Therefore Investment in one account s 5700 and the investment in other account is 7000-5700 = 1300